Arthur Cayley

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Cayley, Arthur

(kā`lē), 1821–95, English mathematician. He was admitted to the bar in 1849. In 1863 he was appointed first Sadlerian professor of mathematics at Cambridge. His researches, which covered the field of pure mathematics, included especially the theory of matrices (see matrixmatrix,
in mathematics, a rectangular array of elements (e.g., numbers) considered as a single entity. A matrix is distinguished by the number of rows and columns it contains. The matrix

is a 2×3 (read "2 by 3") matrix, because it contains 2 rows and 3 columns.
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) and the theory of invariants. The algebra of matrices was the tool HeisenbergHeisenberg, Werner
, 1901–76, German physicist. One of the founders of the quantum theory, he is best known for his uncertainty principle, or indeterminacy principle, which states that it is impossible to determine with arbitrarily high accuracy both the position and
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 used in 1925 for his revolutionary work in quantum mechanics (see quantum theoryquantum theory,
modern physical theory concerned with the emission and absorption of energy by matter and with the motion of material particles; the quantum theory and the theory of relativity together form the theoretical basis of modern physics.
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). The concept of invariance is important in modern physics, particularly in the theory of relativityrelativity,
physical theory, introduced by Albert Einstein, that discards the concept of absolute motion and instead treats only relative motion between two systems or frames of reference.
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. Cayley's collected papers were published in 13 volumes (1889–98).

Cayley, Arthur


Born Aug. 16, 1821, in Richmond; died Jan. 26, 1895, in Cambridge. British mathematician.

Cayley was appointed professor at Cambridge University in 1863. His major works were devoted to the theory of algebraic quadratic forms. He established a connection between the theory of invariants and projective geometry. His studies in this field are the basis for an interpretation of Lobachevskii’s geometry (the Cayley-Klein interpretation). Cayley was also the author of works on the theory of determinants, differential equations, and elliptic functions. He also conducted investigations in spherical astronomy and astrophysics.


Noether, M. “Arthur Cayley.” Mathematische Annalen, 1895, vol. 46, pp. 462–80.
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It wasn't long before Sir Arthur Cayley realised that it would be much harder to prove than anyone thought, outlining the reasons why in a paper that he sent to the Royal Geographical Society in 1879.
The mathematician Arthur Cayley published this as a conjecture in 1879, and in that same year Alfred Kempe published a proof that remained in force until 1890, when an error was discovered.
13 Arthur Cayley (1821-95), the distinguished mathematician (Honorary Fellow of Trinity 1872; Fellow 1875) had his portrait painted in 1874; see DNB XXII, 402.